Question

Please help me with this

Answer 1

`x = 1, \: \: x = (2)/(3)`

Explanation:

`√(3x + 1) - √(2 - x) = √(2x - 1) \\ \\ squaring \: both \: sides \\ \\ ( √(3x + 1) - √(2 - x))^(2) = ( √(2x - 1) ) ^(2) \\ \\ 3x + 1 + 2 - x - 2( √(3x + 1) ) ( √(2 - x) ) = 2x - 1 \\ \\ \cancel{ 2x} + 3 - 2( √(3x + 1) ) ( √(2 - x) ) = \cancel{ 2x} - 1 \\ \\ 3 - 2( √(3x + 1) ) ( √(2 - x) ) = - 1 \\ \\ - 2( √(3x + 1) ) ( √(2 - x) ) = - 1 - 3 \\ \\ - 2( √(3x + 1) ) ( √(2 - x) ) = - 4 \\ \\ ( √(3x + 1) ) ( √(2 - x) ) = 2 \\ \\ squaring \: both \: sides \: again \\ { [( √(3x + 1) ) ( √(2 - x) )] }^(2) = {2}^(2) \\ \\ (3x + 1)(2 - x) = 4 \\ \\ 6x - 3 {x}^(2) + 2 - x = 4 \\ \\ - 3 {x}^(2) + 5x - 2 = 0 \\ \\ 3 {x}^(2) - 5x + 2 = 0 \\ \\ 3 {x}^(2) - 3x - 2x + 2 = 0 \\ \\ 3x(x - 1) - 2(x - 1) = 0 \\ \\ (x - 1)(3x - 2) = 0 \\ \\ x - 1 = 0, \: \: 3x - 2 = 0 \\ \\ x = 1, \: \: x = (2)/(3)`